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Trigonometric Identities

What are different kinds of trig identities?

Questions:

1. If sin x = -1/3, what is cosx?

2. Simplify the expression (sinx + cosx)^2 + (sinx - cosx)^2

3. Verify the identity cotx - tanx = (csc2x - sec2x)/sinxcosx

Solution Preview

TRIGONOMETRIC IDENTITIES

Pythagorean Identities

1. sin2x + cos2x = 1
2. tan2x + 1 = sec2x
3. 1 + cot2x = csc2x

Reciprocal Identities

1. cscx = 1/sinx
2. secx = 1/cosx
3. cotx = 1/tanx

The Tangent and Cotangent Identities

1. tanx = sinx/cosx
2. cotx = cosx/sinx

Identities for Negatives

1. sin(-x) = -sinx (the sine function is an odd function)
2. cos(-x) = cosx (the cosine function is an even ...

Solution Summary

This posting lists trigonometric identities and gives examples of different types of problems that make use of them.

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